Partial Differential Equations in Finance


In this subject, some ordinary differential equations, as well as, some partial differential equations of the elliptic, parabolic and hyperbolic types will be studied. Moreover, the study of some variational inequalities will also be considered.


  1. Ordinary Differential Equations. Exact equations. Integrating Factor.
  2. Partial Differential Equations of the Elliptic, Parabolic and Hyperbolic types.
  3. Sturm-Liouville Problems.
  4. Fourier Series and Transform.
  5. Laplace Transform.
  6. Black-Scholes Equation.
  7. Variational Inequalities.


  • BURDEN, R.L.; FAIRES, J.D. (1993) -- Numerical Analysis (fifth edition), Prindle, Weber & Schmidt, Boston.

  • PINA, H. (1995) -- Métodos Numéricos, McGrawHill.

  • CIARLET, P.G. (1985), Introduction à l'Analyse Numérique Matricielle et à l'Optimisation, Masson, Paris.

  • EKELAN, I. and R. TEMAM (1976), Convex Analysis and Variational Problems, North-Holland, Elsevier, Amsterdam.

  • RAVIART, P.A. and J.M. THOMAS (1983), Introduction a l''Analyse Numérique des Equations aux Derivées Partielles, Masson, Paris.

  • STEELE, J.M. (2004), Stochastic Calculus and Financial Applications, Applications of Mathematics: Stochastic Modelling and Applied Probability, 45, Springer, Berlin.

  • ZAUDERER, E. (1989), Partial Equations of Applied Mathematics (second ed.), John Wiley and Sons, New York.